Let say my algorithm tells me to get the following positions through opening fx positions:
CUR NET POSITIONS
There are 2 ways to achieve this:
- Long 1000 GBP/USD, Long 1000 USD/CHF and Long 1000 CHF/GBP given the rates are 1.310580(GBPUSD),0.999980(USDCHF) and 0.763036(CHFGBP)
- Long 236.96379 GBP/USD and Short 0.02 USDCHF. same rates.
So I replicated the same pl but the first option uses more capital and positions meanwhile the second one is optimal.
I want to develop an optimization that tries to satisfy my required currency positions by using as little forex pairs as possible and minimize the absolute value of exposure as well. I read that Bellman-Ford equations can be helpful in finding the shortest possible way but most of the examples try to find a triangular arbitrage instead of the optimization I am after. Are there any examples out there that I can use or any resource, an idea will be helpful.